Resonant Characteristics Of Three-Level SSSC

SUPPLEMENTARY DAMPING CONTROLLER FOR AN SSSC-COMPENSATED TRANSMISSION LINE

7.2 Resonant Characteristics Of Three-Level SSSC

The study conducted in the previous chapter examined the resonant interactions between the transnUssion line and the generator shaft dynanUcs in the IEEE First Benchmark Model when the line was compensated with a two-level SSSe. In this section, the same investigation will be carried out on a three-level SSSe compensated transnUssion line, once again, using the IEEE First Benchmark Model. For the purpose of convenient referencing, the five torsional modes of the multi-inertia turbine and their associated mechanical natural frequencies, fn, are again shown in Table 7.1.

This study once again considers the same three values of compensating capacitive reactance, Xq*, used in the previous chapter, which are 0.178 pu, 0.275 pu, and 0.3707 pu, in order to investigate a range of operating points.

Table 7.1: Turbo-generator shaft modes in the IEEE First Benchmark Model

Mode Mode Frequency,fn

Mode 1 15.71 Hz

Mode 2 20.005 Hz

Mode 3 25.55 Hz

Mode 4 32.285 Hz

ModeS 47.46 Hz

As in the studies of Chapter 6, the system is initially operating at steady state; a three-phase fault of duration 0.075 seconds is then applied at the receiving-end of the transmission line at t

=

0.1 seconds. The results of four system variables from the PSCADIEMTDC simulation, namely, generator speed, the electrical torque, the LPA-LPB turbine shaft torque and the GEN-EXC shaft torque are shown as follows.

Xq*=0.178pu

In the previous chapter, at a commanded capacitive reactance of Xq*

=

0.178 pu, the resonant frequency, fen in the transmission line caused by the two-level SSSC is 12.8 Hz and the associated subsynchronous complementary frequency, fo - fen is 47.2 Hz. With reference to Table 7.1, the complementary frequency of 47.2 Hz is very close to the Mode 5 mechanical natural frequency of 47.46 Hz.

Fig 7.1 shows the simulated results of the three-level SSSC-compensated line to the short circuit disturbance at X_q*

=

0.178 pu. The results shown in Fig. 7.1 indicate no noticeable destabilization of the system compensated by the three-level SSSC at this value of compensation. With the exception of the electrical torque, shown in Fig. 7.1 Cb), the mechanical system variables exhibit torsional oscillations after the three-phase fault has been cleared, but these are not negatively damped and they are of small amplitude.

(a) Generator Speed

(b) Electrical Torque

~~~

(c) LPA-LPB Torque

¹

~:

(d) GEN-EXC Torque

~ ^0:

-0.50 0.5 1 1.5 2 2.5

Time(5)

Fig. 7.1: Simulated response of the IEEE First Benchmark Mode! to a short circuit fault for the three-level SSSC compensated transmission system at X_q*=0.178 pu.

X_q*=0.275 pu

As predicted in the previous chapter, the resonant frequency,fen in the transmission line caused by an SSSC at a commanded capacitive reactance of Xq*

=

0.275 pu is 19.76 Hz, and the associated subsynchronous complementary frequency, fo - fen is 40.24 Hz. With reference to Table 7.1, the complementary frequency of the system at this value of compensation is half way between the mechanical natural frequencies of Mode 4 and Mode 5.

Fig 7.2 shows the simulated results of the three-level SSSC-compensated line to the short circuit disturbance atX_q*

=

0.275 pu. The results in Fig. 7.2 show that at this value of compensation the torsional oscillations in the mechanical system variables are now of concern: although the oscillations are not noticeably negatively damped, they are larger in amplitude than is the case in Fig. 7.1 and are sustained; such oscillations would in all likelihood reduce the life of the turbine shaft if allowed to persist in this manner. A close analysis of these oscillations (not

shown here) has shown the presence of both the Mode 1 (15.71 Hz) and Mode 4 (32.3 Hz) mechanical natural frequencies.

(a) Generator Speed

~-:E~'

^{5 _ ! I}

^J _J

(b) Electrical Torque

~ ^-:

(c) LPA-LPB Torque

(

~_::E:~~:~

^{o 0.5 1 1.5 2 2.5}

Time(5)

Fig.7.2: Simulated response of the IEEE First Benchmark Model to a short circuitfaultfor the three-levelSSSCcompensated transmission system at Xq *

=

0.275 pu.

X_q*=0.3707 pu

As predicted in the previous chapter, the resonant frequency,fen in the transmission line caused by an SSSC at a commanded capacitive reactance of Xq*

=

0.3707 pu is 30.5 Hz and the associated subsynchronous complementary frequency, fo - fen is 29.5 Hz. With reference to Table 7.1, the complementary frequency of the system at this value of compensation lies in between the mechanical natural frequencies of Mode 3 and Mode 4, but is closer to that of Mode 4.

Fig 7.3 shows the simulated results of the three-level SSSC-compensated line to the short circuit disturbance atX_q*

=

^{0.3707 pu.} The results in Fig. 7.3 show that at this value of compensation

the system is clearly experIencmg negatively damped torsional oscillations. A careful frequency-domain analysis of these results (not shown here) has shown that the mechanical system oscillations are once again multi-modal in character, comprising oscillations at both the Mode 1 and Mode 4 frequencies, but that the Mode 4 frequency is predominant. Thus, at a value ofX_q'

=

0.3707 pu the three-level SSSC results in significant destabilization of the Mode 4 torsional mode as well as provoking noticeable oscillations in Mode 1.

(a) Generator Speed

~_:r;zs;~

(b) Electrical Torque

~t~:===: : ¹

~_:~~

~ O:===~===:J

-0.5o 0.5 1 1.5 2 2.5

Time (s)

Fig.7.3: Simulated response of the IEEE First Benchmark Model to a short circuitfaultfor the three-level SSSC compensated transmission system at X_{q '}

=

^{0.3707 pu.}

The previous three simulation studies have considered the responses of the three-level SSSC compensated transmission system following a three-phase fault, with different commanded compensating capacitive reactance values. The results are in agreement with the conclusions drawn in Chapter Six:

1. Due to the different susceptibility of the torsional modes of a turbine shaft to torsional interaction, it is possible that the close tuning of the subsynchronous electrical

complementary frequency to that of a particular mechanical mode may not, in fact, affect that mode but instead interact with the other modes.

2. Although at some compensation levels the SSSe does not cause instability in the electro-mechanical system, it is evident that it still excites shaft torque oscillations. While this is true in some cases, at other compensation levels, the SS se clearly causes large negatively damped oscillations following a disturbance. Therefore, in the SSR study, it is paramount to examine the resonant characteristics of a compensating device by investigating a range of compensation values.

In the previous three studies it has been shown that, at all of the compensating reactance values considered, the Mode 4 frequency of 32.3 Hz is present in the response of the mechanical system variables following a disturbance, and that it is often the dominant frequency. It is therefore sensible to try and damp out the response of this highly susceptible mode in order to provide stability to the electro-mechanical system. The following section will describe the design of a supplementary controller for the three-level SSSe to damp out Mode 4's torsional oscillations.